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          <h1 class="post-title" itemprop="name headline">经典排序算法总结</h1>
        

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        <h3 id="算法分类"><a href="#算法分类" class="headerlink" title="算法分类"></a>算法分类</h3><ul>
<li>非线性时间比较类排序：通过比较来决定元素间的相对次序，由于其时间复杂度不能突破O(nlogn)，因此称为非线性时间比较类排序。</li>
<li>线性时间非比较类排序：不通过比较来决定元素间的相对次序，它可以突破基于比较排序的时间下界，以线性时间运行，因此称为线性时间非比较类排序。 <img src="/blog/Algorithm_sort/1.png">
</li>
</ul>
<h3 id="比较类排序"><a href="#比较类排序" class="headerlink" title="比较类排序"></a>比较类排序</h3><h4 id="冒泡排序"><a href="#冒泡排序" class="headerlink" title="冒泡排序"></a>冒泡排序</h4><p>冒泡排序是一种简单的排序算法。它重复地走访过要排序的数列，一次比较两个元素，如果它们的顺序错误就把它们交换过来。走访数列的工作是重复地进行直到没有再需要交换，也就是说该数列已经排序完成。</p>
<ul>
<li>比较相邻的元素。如果第一个比第二个大，就交换它们两个；</li>
<li>对每一对相邻元素作同样的工作，从开始第一对到结尾的最后一对，这样在最后的元素应该会是最大的数；</li>
<li>针对所有的元素重复以上的步骤，除了最后一个；</li>
<li>重复步骤1~3，直到排序完成。</li>
</ul>
<img src="/blog/Algorithm_sort/2.gif">
<p><strong>代码实现</strong></p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">public</span> <span class="keyword">int</span>[] sort(<span class="keyword">int</span>[] arr) &#123;</span><br><span class="line">    <span class="keyword">int</span> len = arr.length;</span><br><span class="line">    <span class="keyword">for</span> (<span class="keyword">int</span> i = <span class="number">0</span>; i &lt; len; i++) &#123;</span><br><span class="line">        <span class="keyword">for</span> (<span class="keyword">int</span> j = <span class="number">0</span>; j &lt; len - <span class="number">1</span> - i; j++) &#123;</span><br><span class="line">            <span class="comment">// 相邻元素两两对比</span></span><br><span class="line">            <span class="keyword">if</span> (arr[j] &gt; arr[j + <span class="number">1</span>]) &#123;</span><br><span class="line">                <span class="comment">// 元素交换</span></span><br><span class="line">                <span class="keyword">int</span> temp = arr[j + <span class="number">1</span>];</span><br><span class="line">                arr[j + <span class="number">1</span>] = arr[j];</span><br><span class="line">                arr[j] = temp;</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="keyword">return</span> arr;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<h4 id="选择排序"><a href="#选择排序" class="headerlink" title="选择排序"></a>选择排序</h4><p>选择排序(Selection-sort)是一种简单直观的排序算法。它的工作原理：首先在未排序序列中找到最小（大）元素，存放到排序序列的起始位置，然后，再从剩余未排序元素中继续寻找最小（大）元素，然后放到已排序序列的末尾。以此类推，直到所有元素均排序完毕。<br>选择排序O(n2)的时间复杂度，所以用到它的时候，数据规模越小越好。唯一的好处可能就是不占用额外的内存空间了吧。</p>
<img src="/blog/Algorithm_sort/3.gif">
<p><strong>代码实现</strong></p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">public</span> <span class="keyword">int</span>[] sort(<span class="keyword">int</span>[] arr) &#123;</span><br><span class="line">    <span class="keyword">int</span> len = arr.length;</span><br><span class="line">    <span class="keyword">int</span> minIndex, temp;</span><br><span class="line">    <span class="keyword">for</span> (<span class="keyword">int</span> i = <span class="number">0</span>; i &lt; len - <span class="number">1</span>; i++) &#123;</span><br><span class="line">        minIndex = i;</span><br><span class="line">        <span class="keyword">for</span> (<span class="keyword">int</span> j = i + <span class="number">1</span>; j &lt; len; j++) &#123;</span><br><span class="line">            <span class="comment">// 寻找最小的数</span></span><br><span class="line">            <span class="keyword">if</span> (arr[j] &lt; arr[minIndex]) &#123;</span><br><span class="line">                <span class="comment">// 将最小数的索引保存</span></span><br><span class="line">                minIndex = j;</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line">        temp = arr[i];</span><br><span class="line">        arr[i] = arr[minIndex];</span><br><span class="line">        arr[minIndex] = temp;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="keyword">return</span> arr;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<h4 id="插入排序"><a href="#插入排序" class="headerlink" title="插入排序"></a>插入排序</h4><p>插入排序（Insertion-Sort）的算法描述是一种简单直观的排序算法。它的工作原理是通过构建有序序列，对于未排序数据，在已排序序列中从后向前扫描，找到相应位置并插入。<br>插入排序都采用in-place在数组上实现。具体算法描述如下：</p>
<ul>
<li>从第一个元素开始，该元素可以认为已经被排序；</li>
<li>取出下一个元素，在已经排序的元素序列中从后向前扫描；</li>
<li>如果该元素（已排序）大于新元素，将该元素移到下一位置；</li>
<li>重复步骤3，直到找到已排序的元素小于或者等于新元素的位置；</li>
<li>将新元素插入到该位置后；</li>
<li>重复步骤2~5。</li>
</ul>
<img src="/blog/Algorithm_sort/4.gif">
<p><strong>代码实现</strong></p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br></pre></td><td class="code"><pre><span class="line"><span class="function">function <span class="title">insertionSort</span><span class="params">(<span class="keyword">int</span>[] arr)</span> </span>&#123;</span><br><span class="line">    <span class="keyword">int</span> len = arr.length;</span><br><span class="line">    <span class="keyword">int</span> preIndex, current;</span><br><span class="line">    <span class="keyword">for</span> (<span class="keyword">int</span> i = <span class="number">1</span>; i &lt; len; i++) &#123;</span><br><span class="line">        preIndex = i - <span class="number">1</span>;</span><br><span class="line">        current = arr[i];</span><br><span class="line">        <span class="keyword">while</span> (preIndex &gt;= <span class="number">0</span> &amp;&amp; arr[preIndex] &gt; current) &#123;</span><br><span class="line">            arr[preIndex + <span class="number">1</span>] = arr[preIndex];</span><br><span class="line">            preIndex--;</span><br><span class="line">        &#125;</span><br><span class="line">        arr[preIndex + <span class="number">1</span>] = current;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="keyword">return</span> arr;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<h4 id="希尔排序"><a href="#希尔排序" class="headerlink" title="希尔排序"></a>希尔排序</h4><p>第一个突破O(n2)的排序算法，是简单插入排序的改进版。它与插入排序的不同之处在于，它会优先比较距离较远的元素。希尔排序又叫缩小增量排序。<br>先将整个待排序的记录序列分割成为若干子序列分别进行直接插入排序，具体算法描述：</p>
<ul>
<li>选择一个增量序列t1，t2，…，tk，其中ti&gt;tj，tk=1；</li>
<li>按增量序列个数k，对序列进行k 趟排序；</li>
<li>每趟排序，根据对应的增量ti，将待排序列分割成若干长度为m 的子序列，分别对各子表进行直接插入排序。仅增量因子为1 时，整个序列作为一个表来处理，表长度即为整个序列的长度。<img src="/blog/Algorithm_sort/5.gif">
<strong>代码实现</strong></li>
</ul>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">public</span> Integer[] sort(Integer[] arr) &#123;</span><br><span class="line">    <span class="keyword">int</span> gap = arr.length;<span class="comment">//gap的值</span></span><br><span class="line">    <span class="keyword">for</span> (; gap &gt; <span class="number">0</span>; gap = gap / <span class="number">2</span>) &#123;</span><br><span class="line">        <span class="comment">//对于gap所分的每一个组</span></span><br><span class="line">        <span class="keyword">for</span> (<span class="keyword">int</span> x = <span class="number">0</span>; x &lt; gap; x++) &#123;</span><br><span class="line">            <span class="comment">//进行插入排序</span></span><br><span class="line">            <span class="keyword">for</span> (<span class="keyword">int</span> i = x + gap; i &lt; arr.length; i = i + gap) &#123;</span><br><span class="line">                <span class="keyword">int</span> temp = arr[i];</span><br><span class="line">                <span class="keyword">int</span> preIndex = i - gap;</span><br><span class="line">                <span class="keyword">while</span> (preIndex &gt;= <span class="number">0</span> &amp;&amp; arr[preIndex] &gt; temp) &#123;</span><br><span class="line">                    arr[preIndex + gap] = arr[preIndex];</span><br><span class="line">                    preIndex = preIndex - gap;</span><br><span class="line">                &#125;</span><br><span class="line">                arr[preIndex + gap] = temp;</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="keyword">return</span> arr;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<h4 id="归并排序"><a href="#归并排序" class="headerlink" title="归并排序"></a>归并排序</h4><p>归并排序是建立在归并操作上的一种有效的排序算法。该算法是采用分治法（Divide and Conquer）的一个非常典型的应用。将已有序的子序列合并，得到完全有序的序列；即先使每个子序列有序，再使子序列段间有序。若将两个有序表合并成一个有序表，称为2-路归并。 </p>
<ul>
<li>把长度为n的输入序列分成两个长度为n/2的子序列；</li>
<li>对这两个子序列分别采用归并排序；</li>
<li>将两个排序好的子序列合并成一个最终的排序序列。</li>
</ul>
<img src="/blog/Algorithm_sort/6.gif">
<p><strong>代码实现</strong></p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">public</span> Integer[] sort(Integer[] a, <span class="keyword">int</span> low, <span class="keyword">int</span> high) &#123;</span><br><span class="line">    <span class="keyword">int</span> mid = (low + high) / <span class="number">2</span>;</span><br><span class="line">    <span class="keyword">if</span> (low &lt; high) &#123;</span><br><span class="line">        sort(a, low, mid);</span><br><span class="line">        sort(a, mid + <span class="number">1</span>, high);</span><br><span class="line">        <span class="comment">//左右归并</span></span><br><span class="line">        merge(a, low, mid, high);</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="keyword">return</span> a;</span><br><span class="line">&#125;</span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">void</span> <span class="title">merge</span><span class="params">(Integer[] a, <span class="keyword">int</span> low, <span class="keyword">int</span> mid, <span class="keyword">int</span> high)</span> </span>&#123;</span><br><span class="line">    <span class="keyword">int</span>[] temp = <span class="keyword">new</span> <span class="keyword">int</span>[high - low + <span class="number">1</span>];</span><br><span class="line">    <span class="keyword">int</span> i = low;</span><br><span class="line">    <span class="keyword">int</span> j = mid + <span class="number">1</span>;</span><br><span class="line">    <span class="keyword">int</span> k = <span class="number">0</span>;</span><br><span class="line">    <span class="comment">// 把较小的数先移到新数组中</span></span><br><span class="line">    <span class="keyword">while</span> (i &lt;= mid &amp;&amp; j &lt;= high) &#123;</span><br><span class="line">        <span class="keyword">if</span> (a[i] &lt; a[j]) &#123;</span><br><span class="line">            temp[k++] = a[i++];</span><br><span class="line">        &#125; <span class="keyword">else</span> &#123;</span><br><span class="line">            temp[k++] = a[j++];</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="comment">// 把左边剩余的数移入数组</span></span><br><span class="line">    <span class="keyword">while</span> (i &lt;= mid) &#123;</span><br><span class="line">        temp[k++] = a[i++];</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="comment">// 把右边边剩余的数移入数组</span></span><br><span class="line">    <span class="keyword">while</span> (j &lt;= high) &#123;</span><br><span class="line">        temp[k++] = a[j++];</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="comment">// 把新数组中的数覆盖nums数组</span></span><br><span class="line">    <span class="keyword">for</span> (<span class="keyword">int</span> x = <span class="number">0</span>; x &lt; temp.length; x++) &#123;</span><br><span class="line">        a[x + low] = temp[x];</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<h4 id="快速排序"><a href="#快速排序" class="headerlink" title="快速排序"></a>快速排序</h4><p>快速排序的基本思想：通过一趟排序将待排记录分隔成独立的两部分，其中一部分记录的关键字均比另一部分的关键字小，则可分别对这两部分记录继续进行排序，以达到整个序列有序。</p>
<ul>
<li>从数列中挑出一个元素，称为 “基准”（pivot）；</li>
<li>重新排序数列，所有元素比基准值小的摆放在基准前面，所有元素比基准值大的摆在基准的后面（相同的数可以到任一边）。在这个分区退出之后，该基准就处于数列的中间位置。这个称为分区（partition）操作；</li>
<li>递归地（recursive）把小于基准值元素的子数列和大于基准值元素的子数列排序。</li>
</ul>
<img src="/blog/Algorithm_sort/7.gif">
<p><strong>代码实现</strong></p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">sort</span><span class="params">(<span class="keyword">int</span> a[], <span class="keyword">int</span> low, <span class="keyword">int</span> hight)</span> </span>&#123;</span><br><span class="line">    <span class="keyword">int</span> i, j, index;</span><br><span class="line">    <span class="keyword">if</span> (low &gt; hight) &#123;</span><br><span class="line">        <span class="keyword">return</span>;</span><br><span class="line">    &#125;</span><br><span class="line">    i = low;</span><br><span class="line">    j = hight;</span><br><span class="line">    index = a[i]; <span class="comment">// 用子表的第一个记录做基准</span></span><br><span class="line">    <span class="keyword">while</span> (i &lt; j) &#123; <span class="comment">// 从表的两端交替向中间扫描</span></span><br><span class="line">        <span class="keyword">while</span> (i &lt; j &amp;&amp; a[j] &gt;= index)</span><br><span class="line">            j--;</span><br><span class="line">        <span class="keyword">if</span> (i &lt; j)</span><br><span class="line">            a[i++] = a[j];<span class="comment">// 用比基准小的记录替换低位记录</span></span><br><span class="line">        <span class="keyword">while</span> (i &lt; j &amp;&amp; a[i] &lt; index)</span><br><span class="line">            i++;</span><br><span class="line">        <span class="keyword">if</span> (i &lt; j) <span class="comment">// 用比基准大的记录替换高位记录</span></span><br><span class="line">            a[j--] = a[i];</span><br><span class="line">    &#125;</span><br><span class="line">    a[i] = index;<span class="comment">// 将基准数值替换回 a[i]</span></span><br><span class="line">    sort(a, low, i - <span class="number">1</span>); <span class="comment">// 对低子表进行递归排序</span></span><br><span class="line">    sort(a, i + <span class="number">1</span>, hight); <span class="comment">// 对高子表进行递归排序</span></span><br><span class="line">&#125;</span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">quickSort</span><span class="params">(<span class="keyword">int</span> a[])</span> </span>&#123;</span><br><span class="line">    sort(a, <span class="number">0</span>, a.length - <span class="number">1</span>);</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<h3 id="非比较类排序"><a href="#非比较类排序" class="headerlink" title="非比较类排序"></a>非比较类排序</h3><h4 id="计数排序"><a href="#计数排序" class="headerlink" title="计数排序"></a>计数排序</h4><p>计数排序不是基于比较的排序算法，其核心在于将输入的数据值转化为键存储在额外开辟的数组空间中。 作为一种线性时间复杂度的排序，计数排序要求输入的数据必须是有确定范围的整数。<br><strong>计数排序是一个稳定的排序算法。当输入的元素是 n 个 0到 k 之间的整数时，时间复杂度是O(n+k)，空间复杂度也是O(n+k)，其排序速度快于任何比较排序算法。</strong>当k不是很大并且序列比较集中时，计数排序是一个很有效的排序算法。</p>
<ul>
<li>找出待排序的数组中最大和最小的元素；</li>
<li>统计数组中每个值为i的元素出现的次数，存入数组C的第i项；</li>
<li>对所有的计数累加（从C中的第一个元素开始，每一项和前一项相加）；</li>
<li>反向填充目标数组：将每个元素i放在新数组的第C(i)项，每放一个元素就将C(i)减去1。</li>
</ul>
<img src="/blog/Algorithm_sort/8.gif">
<p><strong>代码实现</strong></p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">int</span>[] sort(<span class="keyword">int</span>[] arr, <span class="keyword">int</span> maxValue) &#123;</span><br><span class="line">    <span class="keyword">int</span>[] buket = <span class="keyword">new</span> <span class="keyword">int</span>[maxValue + <span class="number">1</span>];</span><br><span class="line">    <span class="keyword">int</span> sortedIndex = <span class="number">0</span>;</span><br><span class="line">    <span class="keyword">for</span> (<span class="keyword">int</span> value : arr) &#123;</span><br><span class="line">        buket[value]++;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="keyword">for</span> (<span class="keyword">int</span> i = <span class="number">0</span>; i &lt; buket.length; i++) &#123;</span><br><span class="line">        <span class="keyword">while</span> (buket[i] &gt; <span class="number">0</span>) &#123;</span><br><span class="line">            arr[sortedIndex++] = i;</span><br><span class="line">            buket[i]--;</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="keyword">return</span> arr;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<h4 id="基数排序"><a href="#基数排序" class="headerlink" title="基数排序"></a>基数排序</h4><p>基数排序是按照低位先排序，然后收集；再按照高位排序，然后再收集；依次类推，直到最高位。有时候有些属性是有优先级顺序的，先按低优先级排序，再按高优先级排序。最后的次序就是高优先级高的在前，高优先级相同的低优先级高的在前。<br>        ○ 取得数组中的最大数，并取得位数；<br>        ○ arr为原始数组，从最低位开始取每个位组成radix数组；<br>        ○ 对radix进行计数排序（利用计数排序适用于小范围数的特点）；</p>
<img src="/blog/Algorithm_sort/9.gif">
<p><strong>代码实现</strong></p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">int</span>[] sort(<span class="keyword">int</span>[] array) &#123;</span><br><span class="line">    <span class="keyword">if</span> (array == <span class="keyword">null</span>) &#123;</span><br><span class="line">        <span class="keyword">return</span> <span class="keyword">null</span>;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="keyword">int</span> maxLength = maxLength(array);</span><br><span class="line">    <span class="keyword">return</span> sortCore(array, <span class="number">0</span>, maxLength);</span><br><span class="line">&#125;</span><br><span class="line"><span class="keyword">private</span> <span class="keyword">static</span> <span class="keyword">int</span>[] sortCore(<span class="keyword">int</span>[] array, <span class="keyword">int</span> digit, <span class="keyword">int</span> maxLength) &#123;</span><br><span class="line">    <span class="keyword">if</span> (digit &gt;= maxLength) &#123;</span><br><span class="line">        <span class="keyword">return</span> array;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="keyword">final</span> <span class="keyword">int</span> radix = <span class="number">10</span>; <span class="comment">// 基数</span></span><br><span class="line">    <span class="keyword">int</span> arrayLength = array.length;</span><br><span class="line">    <span class="keyword">int</span>[] count = <span class="keyword">new</span> <span class="keyword">int</span>[radix];</span><br><span class="line">    <span class="keyword">int</span>[] bucket = <span class="keyword">new</span> <span class="keyword">int</span>[arrayLength];</span><br><span class="line">    <span class="comment">// 统计将数组中的数字分配到桶中后，各个桶中的数字个数</span></span><br><span class="line">    <span class="keyword">for</span> (<span class="keyword">int</span> i = <span class="number">0</span>; i &lt; arrayLength; i++) &#123;</span><br><span class="line">        count[getDigit(array[i], digit)]++;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="comment">// 将各个桶中的数字个数，转化成各个桶中最后一个数字的下标索引</span></span><br><span class="line">    <span class="keyword">for</span> (<span class="keyword">int</span> i = <span class="number">1</span>; i &lt; radix; i++) &#123;</span><br><span class="line">        count[i] = count[i] + count[i - <span class="number">1</span>];</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="comment">// 将原数组中的数字分配给辅助数组 bucket</span></span><br><span class="line">    <span class="keyword">for</span> (<span class="keyword">int</span> i = arrayLength - <span class="number">1</span>; i &gt;= <span class="number">0</span>; i--) &#123;</span><br><span class="line">        <span class="keyword">int</span> number = array[i];</span><br><span class="line">        <span class="keyword">int</span> d = getDigit(number, digit);</span><br><span class="line">        bucket[count[d] - <span class="number">1</span>] = number;</span><br><span class="line">        count[d]--;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="keyword">return</span> sortCore(bucket, digit + <span class="number">1</span>, maxLength);</span><br><span class="line">&#125;</span><br><span class="line"><span class="comment">/*</span></span><br><span class="line"><span class="comment"> * 一个数组中最大数字的位数</span></span><br><span class="line"><span class="comment"> *</span></span><br><span class="line"><span class="comment"> * @param array</span></span><br><span class="line"><span class="comment"> * @return</span></span><br><span class="line"><span class="comment"> */</span></span><br><span class="line"><span class="function"><span class="keyword">private</span> <span class="keyword">static</span> <span class="keyword">int</span> <span class="title">maxLength</span><span class="params">(<span class="keyword">int</span>[] array)</span> </span>&#123;</span><br><span class="line">    <span class="keyword">int</span> maxLength = <span class="number">0</span>;</span><br><span class="line">    <span class="keyword">int</span> arrayLength = array.length;</span><br><span class="line">    <span class="keyword">for</span> (<span class="keyword">int</span> i = <span class="number">0</span>; i &lt; arrayLength; i++) &#123;</span><br><span class="line">        <span class="keyword">int</span> currentLength = length(array[i]);</span><br><span class="line">        <span class="keyword">if</span> (maxLength &lt; currentLength) &#123;</span><br><span class="line">            maxLength = currentLength;</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line"><span class="keyword">return</span> maxLength;</span><br><span class="line">&#125;</span><br><span class="line"><span class="comment">/*</span></span><br><span class="line"><span class="comment"> * 计算一个数字共有多少位</span></span><br><span class="line"><span class="comment"> *</span></span><br><span class="line"><span class="comment"> * @param number</span></span><br><span class="line"><span class="comment"> * @return</span></span><br><span class="line"><span class="comment"> */</span></span><br><span class="line"><span class="function"><span class="keyword">private</span> <span class="keyword">static</span> <span class="keyword">int</span> <span class="title">length</span><span class="params">(<span class="keyword">int</span> number)</span> </span>&#123;</span><br><span class="line">    <span class="keyword">return</span> String.valueOf(number).length();</span><br><span class="line">&#125;</span><br><span class="line"><span class="comment">/*</span></span><br><span class="line"><span class="comment"> * 获取 x 这个数的 d 位数上的数字</span></span><br><span class="line"><span class="comment"> * 比如获取 123 的 0 位数,结果返回 3</span></span><br><span class="line"><span class="comment"> *</span></span><br><span class="line"><span class="comment"> * @param x</span></span><br><span class="line"><span class="comment"> * @param d</span></span><br><span class="line"><span class="comment"> * @return</span></span><br><span class="line"><span class="comment"> */</span></span><br><span class="line"><span class="function"><span class="keyword">private</span> <span class="keyword">static</span> <span class="keyword">int</span> <span class="title">getDigit</span><span class="params">(<span class="keyword">int</span> x, <span class="keyword">int</span> d)</span> </span>&#123;</span><br><span class="line">    <span class="keyword">int</span> a[] = &#123;<span class="number">1</span>, <span class="number">10</span>, <span class="number">100</span>, <span class="number">1000</span>, <span class="number">10000</span>, <span class="number">100000</span>, <span class="number">1000000</span>, <span class="number">10000000</span>, <span class="number">100000000</span>, <span class="number">1000000000</span>&#125;;</span><br><span class="line">    <span class="keyword">return</span> ((x / a[d]) % <span class="number">10</span>);</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

      
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              var searchResultList = '<ul class=\"search-result-list\">';
              resultItems.forEach(function (result) {
                searchResultList += result.item;
              })
              searchResultList += "</ul>";
              resultContent.innerHTML = searchResultList;
            }
          }

          if ('auto' === 'auto') {
            input.addEventListener('input', inputEventFunction);
          } else {
            $('.search-icon').click(inputEventFunction);
            input.addEventListener('keypress', function (event) {
              if (event.keyCode === 13) {
                inputEventFunction();
              }
            });
          }

          // remove loading animation
          $(".local-search-pop-overlay").remove();
          $('body').css('overflow', '');

          proceedsearch();
        }
      });
    }

    // handle and trigger popup window;
    $('.popup-trigger').click(function(e) {
      e.stopPropagation();
      if (isfetched === false) {
        searchFunc(path, 'local-search-input', 'local-search-result');
      } else {
        proceedsearch();
      };
    });

    $('.popup-btn-close').click(onPopupClose);
    $('.popup').click(function(e){
      e.stopPropagation();
    });
    $(document).on('keyup', function (event) {
      var shouldDismissSearchPopup = event.which === 27 &&
        $('.search-popup').is(':visible');
      if (shouldDismissSearchPopup) {
        onPopupClose();
      }
    });
  </script>





  

  

  

  
  

  

  

  

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